Gravity : an introduction to Einstein's general relativity

The aim of this groundbreaking new text is to bring general relativity into the undergraduate curriculum and make this fundamental theory accessible to all physics majors. Using a "physics first" approach to the subject, renowned relativist James B. Hartle provides a fluent and accessible introduction that uses a minimum of new mathematics and is illustrated with a wealth of exciting applications. The emphasis is on the exciting phenomena of gravitational physics and the growing connection between theory and observation. The Global Positioning System, black holes, X-ray sources, pulsars, quasars, gravitational waves, the Big Bang, and the large scale structure of the universe are used to illustrate the widespread role of how general relativity describes a wealth of everyday and exotic phenomena. For anyone interested in physics or general relativity. Providing Relevant Solutions Of The Einstein Equation, This Text Introduces Field Equations Of General Relativity & Their Supporting Mathematics. Emphasis Is On The Connection Between Observation & Theory And The Phenomena Of Gravitational Physics. Part I. Space And Time In Newtonian Physics And Special Relativity -- 1. Gravitational Physics -- 2. Geometry As Physics -- 2.1. Gravity Is Geometry -- 2.2. Experiments In Geometry -- 2.3. Different Geometries -- 2.4. Specifying Geometry -- 2.5. Coordinates And Line Element -- 2.6. Coordinates And Invariance -- 3. Space, Time, And Gravity In Newtonian Physics -- 3.1. Inertial Frames -- 3.2. The Principle Of Relativity -- 3.3. Newtonian Gravity -- 3.4. Gravitational And Inertial Mass -- 3.5. Variational Principle For Newtonian Mechanics -- 4. Principles Of Special Relativity -- 4.1. The Addition Of Velocities And The Michelson-morley Experiment -- 4.2. Einstein's Resolution And Its Consequences -- 4.3. Spacetime -- 4.4. Time Dilation And The Twin Paradox -- 4.5. Lorentz Boosts -- 4.6. Units -- 5. Special Relativistic Mechanics -- 5.1. Four-vectors -- 5.2. Special Relativistic Kinematics -- 5.3. Special Relativistic Dynamics -- 5.4. Variational Principle For Free Particle Motion --^ 5.5. Light Rays -- 5.6. Observers And Observations -- Part Ii. The Curved Spacetimes Of General Relativity -- 6. Gravity As Geometry -- 6.1. Testing The Equality Of Gravitational And Inertial Mass -- 6.2. The Equivalence Principle -- 6.3. Clocks In A Gravitational Field -- 6.4. The Global Positioning System -- 6.5. Spacetime Is Curved -- 6.6. Newtonian Gravity In Spacetime Terms -- 7. The Description Of Curved Spacetime -- 7.1. Coordinates -- 7.2. Metric -- 7.3. The Summation Convention -- 7.4. Local Inertial Frames -- 7.5. Light Cones And World Lines -- 7.6. Length, Area, Volume, And Four-volume For Diagonal Metrics -- 7.7. Embedding Diagrams And Wormholes -- 7.8. Vectors In Curved Spacetime -- 7.9. Three-dimensional Surfaces In Four-dimensional Spacetime -- 8. Geodesics -- 8.1. The Geodesic Equation -- 8.2. Solving The Geodesic Equation -- Symmetries And Conservation Laws -- 8.3. Null Geodesics -- 8.4. Local Inertial Frames And Freely Falling Frames --^ 9. The Geometry Outside A Spherical Star -- 9.1. Schwarzschild Geometry -- 9.2. The Gravitational Redshift -- 9.3. Particle Orbits -- Precession Of The Perihelion -- 9.4. Light Ray Orbits -- The Deflection And Time Delay Of Light -- 10. Solar System Tests Of General Relativity -- 10.1. Gravitational Redshift -- 10.2. Ppn Parameters -- 10.3. Measurements Of The Ppn Parameter [gamma] -- 10.4. Measurement Of The Ppn Parameter [beta] -- Precession Of Mercury's Perihelion -- 11. Relativistic Gravity In Action -- 11.1. Gravitational Lensing -- 11.2. Accretion Disks Around Compact Objects -- 11.3. Binary Pulsars -- 12. Gravitational Collapse And Black Holes -- 12.1. The Schwarzschild Black Hole -- 12.2. Collapse To A Black Hole -- 12.3. Kruskal-szekeres Coordinates -- 12.4. Nonspherical Gravitational Collapse -- 13. Astrophysical Black Holes -- 13.1. Black Holes In X-ray Binaries -- 13.2. Black Holes In Galaxy Centers -- 13.3. Quantum Evaporation Of Black Holes -- Hawking Radiation --^ 14. A Little Rotation -- 14.1. Rotational Dragging Of Inertial Frames -- 14.2. Gyroscopes In Curved Spacetime -- 14.3. Geodetic Precession -- 14.4. Spacetime Outside A Slowly Rotating Spherical Body -- 14.5. Gyroscopes In The Spacetime Of A Slowly Rotating Body -- 14.6. Gyros And Freely Falling Frames -- 15. Rotating Black Holes -- 15.1. Cosmic Censorship -- 15.2. The Kerr Geometry -- 15.3. The Horizon Of A Rotating Black Hole -- 15.4. Orbits In The Equatorial Plane -- 15.5. The Ergosphere -- 16. Gravitational Waves -- 16.1. A Linearized Gravitational Wave -- 16.2. Detecting Gravitational Waves -- 16.3. Gravitational Wave Polarization -- 16.4. Gravitational Wave Interferometers -- 16.5. The Energy In Gravitational Waves -- 17. The Universe Observed -- 17.1. The Composition Of The Universe -- 17.2. The Expanding Universe -- 17.3. Mapping The Universe -- 18. Cosmological Models -- 18.1. Homogeneous, Isotropic Spacetimes -- 18.2. The Cosmological Redshift --^ 18.3. Matter, Radiation, And Vacuum -- 18.4. Evolution Of The Flat Frw Models -- 18.5. The Big Bang And Age And Size Of The Universe -- 18.6. Spatially Curved Robertson-walker Metrics -- 18.7. Dynamics Of The Universe -- 19. Which Universe And Why? -- 19.1. Surveying The Universe -- 19.2. Explaining The Universe -- Part Iii. The Einstein Equation -- 20. A Little More Math -- 20.1. Vectors -- 20.2. Dual Vectors -- 20.3. Tensors -- 20.4. The Covariant Derivative -- 20.5. Freely Falling Frames Again -- 21. Curvature And The Einstein Equation -- 21.1. Tidal Gravitational Forces -- 21.2. Equation Of Geodesic Deviation -- 21.3. Riemann Curvature -- 21.4. The Einstein Equation In Vacuum -- 21.5. Linearized Gravity -- 22. The Source Of Curvature -- 22.1. Densities -- 22.2. Conservation -- 22.2. Conservation Of Energy-momentum -- 22.3. The Einstein Equation -- 22.4. The Newtonian Limit -- 23. Gravitational Wave Emission -- 23.1. The Linearized Einstein Equation With Sources --^ 23.2. Solving The Wave Equation With A Source -- 23.3. The General Solution Of Linearized Gravity -- 23.4. Production Of Weak Gravitational Waves -- 23.5. Gravitational Radiation From Binary Stars -- 23.6. The Quadrupole Formula For The Energy Loss In Gravitational Waves -- 23.7. Effects Of Gravitational Radiation Detected In A Binary Pulsar -- 23.8. Strong Source Expectations -- 24. Relativistic Stars -- 24.1. The Power Of The Pauli Principle -- 24.2. Relativistic Hydrostatic Equilibrium -- 24.3. Stellar Models -- 24.4. Matter In Its Ground State -- 24.5. Stability -- 24.6. Bounds On The Maximum Mass Of Neutron Stars -- A. Units -- A.1. Units In General -- A.2. Units Employed In This Book -- B. Curvature Quantities -- C. Curvature And The Einstein Equation -- D. Pedagogical Strategy -- D.1. Pedagogical Principles -- D.2. Organization -- D.3. Constructing Courses. James B. Hartle. Includes Bibliographical References (p. 563-567) And Index. The aim of this groundbreaking new book is to bring general relativity into the undergraduate curriculum and make this fundamental theory accessible to all physics majors. Using a "physics first" approach to the subject, renowned relativist James B. Hartle provides a fluent and accessible introduction that uses a minimum of new mathematics and is illustrated with a wealth of exciting applications. The emphasis is on the exciting phenomena of gravitational physics and the growing connection between theory and observation. The Global Positioning System, black holes, X-ray sources, pulsars, quasars, gravitational waves, the Big Bang, and the large scale structure of the universe are used to illustrate the widespread role of how general relativity describes a wealth of everyday and exotic phenomena. Einstein's theory of general relativity is a cornerstone of modern physics. It also touches upon a wealth of topics that readers find fascinating-black holes, warped spacetime, gravitational waves, and cosmology. Until now it has not been included in the curriculum of many undergraduate physics courses because the required math is too advanced. Using a "physics first" approach to the subject, renowned relativism James Hartle provides a fluent and accessible introduction that uses a minimum of new mathematics and illustrates a wealth of applications. Providing the relevant simple solutions of the Einstein equation, this text introduces the field equations of general relativity and their supporting mathematics. The emphasis is on the phenomena of gravitational physics and the growing connection between theory and observation.